What is meant by "line" is the sequence of actions of a hand. A hand can be played in a multitude of ways. The flop can be check- call, check- raiser, bet-raise-call, etc. When we play, we try to get an idea in advance of our line. If a player has 3bet AA preflop and gets a call, he might say, "My line is going to be bet flop, bet turn and bet river". The same hand can have several "lines". Simply making check-raiser a flop instead of betting it will change the line.
If you're discussing poker with friends, you can tell them about a hand you've played and want to get advice on. You can tell them how you played the hand and you can ask them, "How do you like my line here"? Your friends will then be able to suggest alternative lines. Think of the line as just one of many ways to play a hand. The right line to take will depend on many factors. For example, if you have a very strong hand and you are up against a bluffer who likes to bet when you pass, it will be better to have a passive line than an aggressive line.